摘要
The aim of this paper is to establish a mathematical fundamental of complex duality quantum computers(CDQCs) acting on vector-states(pure states) and operator-states(mixed states),respectively.A CDQC consists of a complex divider,a group of quantum gates represented by unitary operators,or quantum operations represented by completely positive and trace-preserving mappings,and a complex combiner.It is proved that the divider and the combiner of a CDQC are an isometry and a contraction,respectively.It is proved that the divider and the combiner of a CDQC acting on vector-states are dual,and in the finite dimensional case,it is proved that the divider and the combiner of a CDQC acting on operator-states(matrix-states) are also dual.Lastly,the loss of an input state passing through a CDQC is measured.
The aim of this paper is to establish a mathematical fundamental of complex duality quantum computers（CDQCs） acting on vector-states（pure states） and operator-states（mixed states）,respectively.A CDQC consists of a complex divider,a group of quantum gates represented by unitary operators,or quantum operations represented by completely positive and trace-preserving mappings,and a complex combiner.It is proved that the divider and the combiner of a CDQC are an isometry and a contraction,respectively.It is proved that the divider and the combiner of a CDQC acting on vector-states are dual,and in the finite dimensional case,it is proved that the divider and the combiner of a CDQC acting on operator-states（matrix-states） are also dual.Lastly,the loss of an input state passing through a CDQC is measured.
基金
supported by the National Natural Science Foundation of China (Grant Nos. 10571113 and 11171197)
the Fundamental Research Funds for the Central Universities (Grant No. GK201002006)
